Drill is part of the military, they do a lot of sharp walking with rifles, flags or just like that, so Drilly is when you wake up in the morning and that you feel like you need to drill, not especially because you like it, but it is because you are too use to it. You also feel drilly when you wake up in the morning and you have dreamed about drill during your night.

-Oh, I feel drilly this morning!
-Let's form up guys it's gonna be an hard day...